Monogenic fields are the emphasis of Clifford analysis and many of the theorems of holomorphic functions in complex analysis apply to these fields. Once again, on the unit disk \(\mathbb {D}\)  take \(f_+ = f_0 + f_2 \)  then if \(f_+ =0\)  we can use eq:gradofplanespinor to derive the Cauchy–Riemann equations


f0x1 = f2x2  f0x2 = -f2x1

which shows the function \(z\)  is indeed monogenic. For more detail on the relationship of monogenic spinor fields to complex holomorphic functions see Doran and Lasenby [1]}.
